#geometry is the only part of mathematics that i comprehend

[giulliadella]

OK, so I am definitely insane, but I ABSOLUTELY needed to find out how much approximately would Bill Cipher weigh. It's 2AM and I finished my calculations, so here we go.

First of all, I had to assume what his exoskeleton is made of and I think it's silica (or quartz, SiO2). I think this for 2 reasons:

Bill turns to stone when he dies, so that means that his physical form had to be made of stone at least partially and

He likes to eat glass and glass is made of SiO2, so I think he needs to do that to keep his exoskeleton/shell healthy, like snails eat calcium.

So, then I went to see how much animals with SiO2 skeleton weigh. Those animals are glass sponges from class Hexactinellida, the largest of which contain up to 50kg of silica. These sponges are cylindrical with large opening on top, so I took the dimensions of the largest sponges (1.4m wide and 2m tall) and calculated their surface area which was 23.73 square meters.

Then, I calculated Bill's surface area. Bill is an equilateral triangle (because Axolotl said that all his angles are 60 degrees), but he also has some depth, so he's actually a very thin pyramid. From the comic it looks to me that his sides measure about 30cm (0.3m) and for the sake of easier calculations, let's say that he's 1cm (0.01m) thick. After a lot of calculations, I came to the conclusion that his surface area is 0.165 square meters.

So, if a sponge of surface area 23.73 square meters has 50kg of silica, Bill with his 0.165 would have 0.35kg of silica.

But that's just silica. Bill also has muscles and other components. I don't think that he has bones, so I'm going to calculate his volume (that's 0.0026 cubic meters of triangle + a little bit that make his arms, legs and hat, which is also a part of him) and fill it with muscle tissue. Muscle density is 1.06kg/1 cubic meter, so Bill's 0.0026 cubic meters would have 0.0028kg of muscle.

So in total, Bill would weigh 0.35kg +0.0028kg= 0.3528kg, so a little bit over 350 grams. In Burgerland measures that's 0.77 pounds.

Now that's if his exoskeleton is JUST silica. If it has more, like sponges do, than it could weigh up to 4.17kg! (because the whole sponge weighs 600kg).

In conclusion, Bill could be as light as 350 grams (0.77lbs) or as heavy as 4.5kg (10lbs) if we calculate just muscle. I am not adding fat or any other tissue because HOW THE FUCK CAN ANYBODY EXPLAIN FAT DISTRIBUTION OF A TRIANGLE!?

And this, dear people, is what I'm using my biology degree for. pls kill me

Weekly Test

(casual)

[spacemiddenzz]

so i was watching @super-metroid's stream of Jimmy and the Pulsating Mass (highly recommend by the way) and she fought Imaginary Numbers this time. I guess I just wanted to share my thoughts on it, since it's my favorite boss and all. This is gonna be a longpost and it's gonna have spoilers so the whole thing can be found under the cut.

So, to put it simply, this dungeon is about stress and confusion. It's about Jimmy's mind frantically trying to comprehend the high-level math that Andrew is teaching him on top of his schoolwork. Jimmy thinks that his dad is the smartest man in the world- this is hyperbole for sure, but the fact that Andrew is quite intelligent remains clear. Jimmy looks up to Andrew because of his intelligence- and because of this it means a lot to Jimmy to be praised by Andrew. He wants his dad to view him as intelligent as well, because, if a man as smart as Andrew thinks Jimmy is smart, he can't be wrong! And hell, it feels nice to be validated by your parents.

Clearly, Andrew has already recognized Jimmy's talent with numbers and has started teaching him concepts beyond the second-grade curriculum, something that we see in the flashbacks in the Symmetrical Cavern. However if Imaginary Numbers' design is anything to go by, these concepts may be at or above the high school level. They're too much for Jimmy to understand. He's only eight, and his mind just isn't ready for that yet. Still, he feels the pressure to keep up with- and understand- the work that Andrew gives him. Why? Because he fears failure. He worries that if he admits to his father that the work is too hard, Andrew won't see him as a "smart boy" any longer- and that praise and validation means a lot to Jimmy. He doesn't want to lose it.

Let's start with the song that plays during this nightmare dungeon- Counting Backwards From Infinity. From the erratic bassline to the random samples of people shouting numbers in no particular order over and over again, this song simply screams disorder and panic. As a person who has always struggled with math, it's incredibly relatable. Counting Backwards From Infinity always reminded me of taking math tests in high school. I was so slow that I almost never could finish a test in a single class period. The frantic, wild bass and the cacophony of people screaming numbers out of order reminded me of trying desperately to remember how to solve a type of problem- and do it quickly enough so that I could hand the test in before the bell rang. I imagine that this is how Jimmy feels when Andrew places in front of him a concept that the boy does not fully understand. Perhaps he's had it explained to him several times but still can't fully grasp it (likely because, again, the kid is eight). The wild confusion and stress he feels when he doesnt fucking understand what's in front of him and doesnt want to look like an idiot in front of his dad. Even the name of the song is a reference to the fact that at this stage of his life this stuff may be an insurmountable task.

The dungeon itself is also set up in an incredibly confusing way. There's a bunch of bizarre-looking purple structures and winding paths. You teleport all over the place with no particular rhyme or reason. The enemies in this area, too, are deformed geometrical shapes that are almost Lovecraftian in the way that they cannot be understood. To Jimmy, Andrew's teachings might as be as comprehensible as a Lumpagon or a Squiggles, and that's definitely the idea that one gets here. The confusion, the pressure, the panic.

At one point in the dungeon you're teleported to a fakeout area that looks like the Path of Enlightenment. This is my favorite thing about the Asymmetrical Cavern, because of the fact that it has so many cool secrets, but also because it gave me a feeling that I could (once again) relate to. Jimmy's teleportation to the Path of Enlightenment isn't random. It represents familiarity in a sea of confusion. Jimmy sees something he recognizes during Andrew's lessons. Maybe he thinks that he's finally got the hang of it- that he's studied hard enough and now all of this jargon makes sense- only to be rudely awakened by the fact that he's been doing it wrong and never understood the concept in the first place. Even the secrets kind of hint at this. If you speak to pointman in this part of the dungeon he says "I am the blood of numbers leaking from your ears. The nails of ignorance are already being driven into your brain. What point is there in giving voice to madness?" (which is metal as fuck by the way)

Jimmy just thinks that his inability to understand makes him an idiot. His lack of understanding- the nails of ignorance- are being driven into his brain. If he can't understand all of Andrew's teachings, maybe he was never a smart boy after all.

And finally let's talk about Imaginary Numbers itself. First of all, it's an amalgamation of a bunch of different mathematical symbols, including a tombstone, a slashed epsilon, and a sigma. I'm sure there are more, but those are the only ones I recognized, honestly. Given that dreams don't really make things up, instead just taking things that you have seen/experienced before, it looks like Jimmy has encountered some... seriously advanced shit. Tombstones are used in geometric proofs. I only started doing proofs in high school geometry, meaning that Jimmy may very well be learning concepts meant for kids twice his age. No wonder the poor kid is stressed.

Oh yeah, also the boss sucks ass to fight. I've heard some people call that bad game design, but I'm not sure that's how I'd classify it. Sure, like I said, the boss sucks complete ass to fight and is almost entirely RNG-dependent. From a gameplay standpoint, this is wack as hell, yeah. Fucking 30% chance to deflect any magical or physical attack with a 30% chance to dodge a physical attack on top of that? Definitely bad game design. But from an artistic standpoint? Not at all. In fact, the futility of this fight adds to it. It really drills into your head that the only thing on your side here is pure fucking luck. And the odds aren't in your favor.

The feeling of futility- of the fact that this may in fact be, by all definitions, an insurmountable task for Jimmy, really struck home the situation. The battle would not be nearly as impactful without this. And personally, I'm all for it. Imagine walking into the Asymmetrical Cavern for the first time, not knowing what to expect. You get your ass handed to you on a silver platter by Imaginary Numbers after it chains Program Omega at you five times in a row.

That's the feeling Kasey wanted to give you. And it's critical. It's just... so perfect, I honestly don't know how to put it into words. It was supposed to represent the confusion and turmoil of a task nigh insurmountable. And it did the job pretty damn well, if I do say so myself.

I know Jimmy is good at numbers and this wasn't supposed to represent a real struggle with the subject of math/the concept of numbers in general, but hot damn if I didn't feel seen. Except Jimmy is eight but I was like 17 struggling in precalc with the same shit. I guess we know Jimmy's smarter than I am rip

TLDR; andrew please stop putting unnecessary stress on your kid youre freaking him out

anyway if you guys have any thoughts about this boss or this dungeon in general i would love to hear them. but where im at its like 2 AM so im probably gonna it the mf sack for now. later dudes

[wisdomrays]

TAFAKKUR: Part 298

THE INVISIBLE SCRIPT ON THE VISIBLE : MATHEMATICS

Af you follow scientific magazines, you may have realized one thing: articles on mathematics are seldom published in such magazines. The major reason is that, in a way, mathematics is a world which is difficult to comprehend, a world where abstract logic is embodied in concrete statements. It cannot be said to be popular among people except for mathematicians, for it is thought to lack a literary side and emotional appeal, and to be rather uninteresting. Mathematics draws the attention of those who try to understand the universe and the reason of creation; it fulfils this duty by unveiling the secrets of creation.

In a book that deals with questions of logic, when we see numbers written in succession, such as 5, 15, 25; then we are able to discover the relation between these numbers, to predict the next number and to realize that this pattern was made by somebody. However, if we were to be told that these figures indicate the distance covered in equal segments of time by a pebble that has been dropped from a certain height, most of us would not think about the One Who made this general rule.

Or for example, the equation 11.111.111 x 111.111.111 = 12.345.678.987.654.321 may be as amazing to some people as the verses of a beautiful poem, whereas it will leave others cold.

Likewise, the famous mysterious symbols of mathematics, e, i, , are nothing more than some alphabetical signs for most of us, nevertheless they must have meant a lot to the famous physicist, Richard Feyman, since he wrote the following equation in his diary, noting that he admired it: ei+1=0

If we write f (z) = Z2 + c;, this will not be a meaningful sentence for most people. But that will not change the fact that it is an incredibly simple expression of biological and physical reality in an expression which concerns our lives (as in fractal logic). And the picture you see here is nothing but the analytical projection of this equation on a computer screen.

The spiral form which can be seen in various things from cone shells to nebulas, has a very simple formula, r2=a2/A which is fascinating for those who spend some time to think about it. All these examples have a point in common. These numbers, which are abstract concepts, are as real as the concrete objects of the physical world. While other sciences make sense, more or less, for a layperson, mathematics can only be appreciated by people who know it well.

The mythological Princess Dido of Phoen-icia fled from the city where her husband (the King;s brother) had been slain by the King. She wanted to settle in Carthage, in North Africa. There the King only allowed her to buy as much land as could be covered by the skin of a cow. Dido decided to interpret the word ;cover; in a wider sense. She had her servants cut the skin in thin strips, connecting them to each other. In the end, she obtained a long cord, estimated to be somewhere from between 1,000 to 2,000 m. long. When it came to placing it on the ground, Dido wanted to find the shape that would cover the largest area. She found the right shape. She made a circle on the ground and she was able to encompass quite a large area of land. As a matter of fact, looking at some ancient castles, we can understand that they were built in this way in order to create the largest structure over the smallest possible area. This explains why the cross-section of a vessel tissue is circular, because it occupies minimal space in the body.

Did you know that mathematical reality applies in our body and in the universe? This fact was realized when scientists developed fractal geometry. The fractal structure we see in the roots and leaves of plants and in the human respiratory and vascular systems are very good examples of this fact. Such excellence indicates the All-Knowing Omnipotent One Who is behind these geometrical designs.

What is the invisible secret of this visible structure? Dido had to enclose the maximum area by using limited material, which she accomplished. Such optimization also exists in the human body and in other living things. The biological systems we have mentioned above have vessel systems designed as fractal networks, delivering the necessary substances to cells. Essentially, these systems are designed in such a way that the vessels occupy minimal space while serving all the cells within the system; this can only be realized through such a fractal structure.

The most striking proof supporting this idea is that if the human veins, which do not take up a great deal of space in the body, were all added together, they would reach a length that is three times the circumference of the world.

How can this be possible? This can be explained quite simply: find an equilateral triangle and carry out the following instructions. First, divide each side of the triangle into three equal sections and place another (smaller) equilateral triangle on the middle section of each side you have divided, facing outwards. If you repeat the same thing for each of these small triangles, you will create the pattern below.

In a fractal structure, as the number of branches near infinity, the shape of the structure resembles a circle more and more. The new area we will find cannot be bigger than the area of the circle, and the points of contact with the circle will approach the maximum value.

We can also explain this fact in the following way: take a circle with a radius of 3 cm. This will serve as the cross-section of a cylindrical object. Then draw seven smaller identical circles inside the first circle. You will see that the proportion between the sum of circumferences and the sum of areas is 5/7. Those who are interested in mathematics will see that as the value of the r (radius) decreases, the difference increases. This clearly indicates that fractal structures are always advantageous. So, what about organs like the brain or the lungs? They do not have a completely fractal structure, yet they really need to have a larger surface area than other objects of equal size. These organs have been enabled to have the largest possible surface area by being convoluted. Otherwise, man would be a strange creature, burdened with a huge mass on his back. Similarly, when we look at a map that shows the coastlines, we see that a coastline that has many capes and bays has a longer coast line than its counterparts, which run straight along the land. All these living things or organs (man, trees, brain etc) have such structures from the very moment they are created. This system or project (Figure 10) cannot have developed on its own, by chance, without there having been a Creator.

Sir James Jean says, ;The Creator must be a perfect Mathematician; in his book The Mysterious Universe. In so saying, he draws attention to mathematics, the mysterious pattern in the universe, and points to the Artist behind the ornamented beauty seen in Creation. The magical science of mathematics whispers its secrets to those who try to perceive it through the eyes of wisdom.

[kalosophia]

The Philosopher’s Standard Of Truth

What do I say is the philosopher’s standard of truth? It is one that makes no reference to physical phenomena, except perhaps by analogy, in order to help reveal a general and comprehensive principle, i.e. a sameness and permanence amid the flux of matter. But, primarily, it makes reference to mental order: the order that is mind. This is not about making arguments that are logically sound, as a logically true statement may have false premises, but rather seeing if what follows from a line of reasoning is, in fact, reasonable. People commonly say words to the effect of “that has the ring of truth” or “that doesn’t quite ring true” by which they mean that a line of reasoning either conforms to some internal standard or does not; either it’s consistent, well-formed and orderly, or not.

The human mind, when sound, is attracted to order, harmony, simplicity, elegance, beauty and things of a kindred nature because it finds such things in itself. Indeed, it is a self-directed measure of such things. It has the ability to comprehend anything it apprehends in some bound and number and with a sameness of conception that can be communicated to others. Differing opinions may cloud the exactitude of mental conception, but humankind relies on a set of foundational understandings, or common conceptions, in order to apprehend, think, and communicate. What is this mental foundation upon which humankind depends? What is this nexus of understanding, meaning and mathematical certitude?

Philosophical men and women have proposed that the human soul is a microcosm of the macrocosm, crudely put a “copy” or image of the universe, composed of all of the “reasons” on a micro scale that the universe contains on a macro scale. And referring to the above arguments, we are not here speaking physically, but rather mentally and psychically, if we’re not ashamed to admit psyche, or soul, to our thinking, which indicates the vital “breath”.

That the language of the physical universe is mathematics, is a truth that many intelligent men and women easily affirm, as it is universally applicable, discoverable, and demonstrable, and exquisitely reliable. But how comes this astonishing sameness among the difference, flux and seeming chaos of the physical universe? How is it that we can apprehend and contact this pre-physical world? And what does this have to do with the standard of truth discussed above?

Perhaps there is more to this world of incontrovertible reason and exactitude than only number and geometry, which we readily admit as true despite not being able to see them. There is much in the world of human experience and meaning that’s relegated to the merely subjective that nevertheless has a sameness of subsistence that makes it communicable in language and argument. Notions such as sameness, difference, motion, permanency, being, wholeness, parts, vastness, diminution, infinity, boundary and many more have definite meanings and applicability. All of this points to the truth that human minds share “mind” in common and mind is a world of order and reason that corresponds both to mind itself and to each individual mind. And it is mind itself that is the standard of truth.

So, when the human mind is working well in its investigation of truth it is imitating the mind of the universe. The Platonic tradition discovered, named and perfected a mode of thought that adapts the individual mind to its author and exemplar in the greatest degree possible. That is, the skill, art, and science of dialectic, which views the whole universe of being and mind as one that is orderly, proceeding from the simplest of underlying realities to the more complex through a process of abiding, procession, and conversion; a circular motion and pattern of providence that applies to all things. Philosophers who place their trust in dialectic believe that all things follow beautifully from their causes and are converted back to them through a process of similitude, meaning that causes always bring forth similar things prior to dissimilar. It is through a belief that from certain things other certain things must follow, that philosophers are able to attain to truth in their reasonings. Truth in the human mind being a conformity of conceptions with things themselves.

But what is this conformity of conceptions to real beings? Is it not the mind of the philosopher becoming those things by participation? Being caused by the intelligences of those things, in conjunction with reason, in the fullest degree possible? And how does the philosopher approach to these intelligences in order to be filled? First, they must retire within in order to be informed by physicality and human opinions in the least degree. Then to apply themselves to the desired object of knowledge by the pure motions of the mind which imitate the pattern of progression and conversion apprehended in real beings, and which we are mapped to in our very essence, as microcosms of the macrocosm. These pure motions of the mind are entirely natural to humanity and are not evident in irrational animals. In the Platonic tradition, they have been called definition, division, demonstration, and analysis. These motions are inter-related and never divorced from one another, though their powers are distinct and can be applied in the investigation of truth by an attempt to reasonably follow the implications of any assertion.

— Kieran

[tofathomtheunfathomable]

2. A Model of the Human-Soul Entity

First of all, I want any reader to know that I am not a philosopher, nor an official of any religious group or organization. So what am I, what are my credentials? I do not believe I require any since I consider myself simply a storyteller. In this role, I do not have to produce any proofs to substantiate my tale, nor cite any references. Anybody who wishes to obtain additional details can always use their minds to search for more and/or better insights into what I wish to communicate. It is out there. But for right now, let the tale begin. 

As far back as I can determine many humans have held the view that they are not simply another mammal. They believed that they possessed an additional inner quality, which is quite difficult to define and impossible to understand - something commonly referred to as a soul. Whether the soul exists or not has been debated extensively, but I have not yet come across anything definitive, which might prove or disprove this presumption.

What I wish to present here is a model of how a soul might interact with its human “host,” what some of its functions might be and what the purpose of such an arrangement might involve. 

In my model, the human body and the soul had their origins in two completely different realms. The body is of course part of our material world, with which we all are intimately familiar. In contrast, the soul hails from what I would like to refer to as the “Spiritual Realm.” What is this realm like? It has no time, no space, no matter, no light, i.e. it does not possess anything in common with our physical world. It is emptiness, completely void of anything material, a concept that is very difficult, if not impossible for us to visualize and comprehend. 

While the material world and the spiritual realm are the sole constituents of this model, one can easily visualize additional distinct realms being made up of mixtures of these two that could serve as intermediary realms, connecting the two end points. This would be analogous to the Ying (white) representing the spiritual realm and Yang (black) the material world and various shades of grey connecting the two. Since the formal introduction and inclusion of such intermediate realms would only render the model much more complex and hence more difficult to develop, let me for now limit this model to the two realms at either ends of such a possible spectrum of realms.

For reasons to be alluded to later, souls need to become part of a human being, a union that will persist throughout the body’s life time. The soul attempts to achieve the most optimal outcome of such a relationship. To this end it will “select” its host based on the spiritual environmental conditions, in which that human will most likely spend its life. 

It is interesting to note at this juncture that many religious and spiritual groups believe that humans possess three spiritual “power” centers: the mind, the spiritual heart and the seat of willpower. In general, these are fundamental properties of spiritual entities. Hence they may very well be intrinsically parts of the soul, rather than the physical body.

When the soul joins its human partner, these three features permeate the human body and will continue to do so until the body is deceased and the union is dissolved. Another interesting conjecture is that the humanoid mammal did not possess these three spiritual qualities. It was only when the first union of a soul with such a mammal occurred that what we now refer to as a “human” came into existence. 

So why does the soul require such a quasi- symbiotic relationship with a material entity in the first place and what role does each one of these components play? 

To describe this precisely in human terms is quasi impossible and hence I will employ one of the oldest and most important tools of storytelling: the use of parables, allegories, metaphors, symbols and analogies. These might allow us to get an idea of how something like a soul-human entity might function in practice, even though it can be intrinsically very difficult or almost impossible to be described in “real” terms. In our context, the analogy used to describe the union between the soul and its human is that of an old fashioned player-piano. Such an instrument could be played either like an ordinary piano by a pianist or it could play “by itself.” In the latter mode, it was fed a roll of paper with protrusions signaling to the instrument, which particular keys were to be struck at any given time to produce the sounds that were supposed to be heard. To produce the paper roll with the protrusions, the process is reversed. A pianist sits at the instrument and plays a melody and each time keys are depressed, protrusions are made in the appropriate positions onto the paper roll.² This is the analogy and it “translates” in the soul-human situation in the following way: the human’s role is that of the piano cum pianist, while the soul functions as the paper roll, the record of what has been played. This arrangement is vital, since in this model the soul IS the music, but cannot produce it. For this it needs the human. 

It might be appropriate at this juncture to explain why I reached back to this old-fashioned type of player piano rather than cite a modern version of such an instrument. Yes, both types operate essentially identically, with only the paper roll having been replaced by an electronic device. However, the old-fashioned instrument is much more graphical and hence easier to understand than the modern version, where all the critical storage elements are concealed in a black box. 

It is not important when exactly the soul joins its human partner, at the time of its conception or its birth (though it is probably the former). The music is the metaphor for the whole spectrum of activities a human will engage in during its life. 

In the 17th century, a British philosopher, John Loke (1632-1704) espoused the concept that the memory and hence the mind of a newborn is like a blank slate. Whatever is written upon it is then due to the external experiences it has during its lifetime. In my model, the soul, which is, after all, the depository of everything it had experienced and learned in all its previous incarnations, will connect to and interface with the newborn’s brain, which is the gateway to the human’s physical body. After this connection is established, the physical body can access the soul’s mind, which then, for all practical purposes, becomes its mind as well. This process will most likely not occur instantaneously, but in an orderly, timely fashion. Or, in terms of Locke’s analogy, the mind of the soul will initially write on the baby’s slate. After this process is completed, external experiences will be the principal sources writing on the slate. There could very well be a time when both of these sources might write on the slate simultaneously.

Such a process could account for a seemingly strange phenomenon observed in many people. For instance, students in mathematics are introduced to new subjects, such as arithmetic, algebra, trigonometry, geometry, complex variables, statistics, calculus, etc. over the course of their studies. Generally, these subjects will become more and more taxing and challenging to the students as new ideas are encountered. Certain individuals may find some of these subjects a breeze, easy to deal with and to comprehend as if they were something they had encountered previously, even though there is no evidence that this could have happened in their present existence. Then suddenly, everything changes. They suddenly face completely new, often alien, ideas and concepts, something they had neither seen nor heard of previously. Might this be because the soul itself had never encountered these new concepts in its prior incarnations and that they were thus not in its database? If so, they could of course not have been in the shared mind.

Now let us return to our player-piano analogy. Eventually, the soul has finished its “downloading,” a process corresponding to the paper roll having reached the end of the protrusions that had been made on it in previous incarnations. From that point on, the human being becomes the pianist who now plays the instrument, which in turn makes a whole new set of protrusions on the paper roll. This then represents a complete record of everything that the human has done during its life. At death, all the non- physical essence of the human (represented by the “music” it has composed during its lifetime) is now part and parcel of the soul, which then departs this world and will go to one of the intermediary realms to which I alluded earlier. I shall refer to this region as “the Realm of the maturing Souls.” This is a place where souls are still loosely connected to our material world, but in a much more tenuous fashion. In this realm the souls are able to “digest” what they have experienced and plan their next steps. Finally, in the fullness of time the whole process will be repeated in the soul’s next incarnation. This will be repeated over and over again, until the soul has reached its goal and is empowered to leave this material world completely, if it so desires. Before it returns to the Spiritual Realm, the record of all the music on the paper roll is transformed into a completely non-material form: the essence of the soul, a purely spiritual entity once again. A metaphor for this process can be found in science where a special mathematical procedure is used to reduce a two-variable function into a single-variable function. In the case of wave-like phenomena like music, the result is often then referred to as a “frequency spectrum.” This then is the analogy to what the soul IS in the Spiritual Realm. 

This represents the rough outline of the model I utilize in my attempts to visualize and comprehend the soul-human relationship and thus cast some light on the spiritual entity we call the soul. This is not a comprehensive model by any means and I hope that readers will be able to improve it or develop alternative models to shed yet more light on this spiritual-material union. 

___________________________________________________________

² For those readers who might not be too familiar with a player- piano, a short clip of how it works can be found on YouTube’s website by following this link.

[liliannorman]

Lack of diversity in his field has troubled this mathematician

Reaching the top ranks of mathematicians isn’t easy, even when you’re really smart. But Edray Goins managed just that. He works at the intersection of algebra and number theory. He likes studying so-called Diophantine equations. These have certain patterns of integers. One example: “Pythagorean triples,” such as the 3-4-5 right triangle, where three squared plus four squared equals five squared. And don’t worry if you don’t understand that — many adults don’t, either.

In his career, Goins has worked at some of the top universities for math, such as Caltech, Stanford University and Harvard University. But he noticed something. At every one of them, there were few women and minorities, especially Blacks and Latinos. “It’s always depressed me,” Goins says. “I complained about this over the years, saying this isn’t right. Something needs to change. But I realized I can’t complain unless I’m willing to do something about it.”

So last year, Goins took a job as a professor at Pomona College. It’s in Claremont, Calif., not far from where he grew up. He’s still tackling those complex math problems. But his real goal is to help train the women and minorities in college who will be the next generation of scientists and mathematicians. In this interview, Goins shares his experiences and advice with Science News for Students. (This interview has been edited for content and readability.)

What inspired you to pursue your career?

When I was in elementary school, the space shuttle was launched for the first time. Watching that got me fascinated with science and how the world works. 

And so, when I went off to college at Caltech in Pasadena, Calif., I majored in physics. During the first few weeks, I saw a book at the campus bookstore entitled Algebraic Geometry. I knew what algebra was. I knew what geometry was. But I’d never heard of “algebraic geometry.” I purchased the book and tried to read it. I saw a few pictures in there that looked pretty but couldn’t comprehend what I was reading.

I purchased a second book, An Introduction to Number Theory. Again, I had no idea what this was. I started to read. One day my calculus teacher said there’s a guy named Harold Stark coming to Caltech to give a series of lectures. This was the guy who wrote the book I was reading — the book about number theory. So I went to the talk. I understood maybe the first 45 minutes. After that I had no idea what he was talking about. But that book and the guy discussing what was in that book — that’s what convinced me to be a math major.

How did you get where you are today?

At first, I was embarrassed to tell people I was majoring in math. I did it to indulge in the subject. I kept the physics major because I figured I could be a physics professor and do research in physics. That was something I could see myself doing. But I didn’t understand the career paths of someone who majored in mathematics. I didn’t tell anyone I was a math major until maybe my third year of college.

I felt very fortunate to be at Caltech. Some of the world’s best physicists were teaching there. For example, Kip Thorne — who won the 2017 Nobel Prize in physics for helping discover gravitational waves — worked on all of this while I was an undergraduate. Seeing that when I was 18, 19 years old motivated me to become a scientist to change the world. I didn’t just want to get A’s in my classes. I wanted to make a huge discovery, to do something that had never been done before.

Edray Goins celebrates with his mother after completing his PhD in mathematics at Stanford University in 1999.Courtesy of E. Goins

Then I went to Stanford, in California, for graduate school. I had the time of my life. By my second year or so, I decided I would be a math professor.

To keep one foot in the physics world, I’d also been going to the National Society of Black Physicists conference every year since I was a sophomore. One year it was held at Stanford. As the conference was winding down one night, it was just me and Stanford physics professor Doug Osheroff sitting at a table. I was very intimidated because he had won a Nobel Prize some years before. But you know, he was just trying to be encouraging to people at the conference.

We got to talking, and I told him I was embarrassed that I wasn’t a physics major anymore. I didn’t think I was very good at physics. He asked me about the training I had as an undergraduate. He stopped me at one point and said that I was so good I could’ve entered grad school as a third- or fourth-year PhD student. 

No one had ever told me that I was that good. That really gave me a lot of confidence. And now I was saying, “I can really do this.”

What’s one of your biggest failures, and how did you get past that?

I don’t know if “failure” is the right word, but if I could do it all over, there are two things I would do differently. One, I think, is having a family, having kids. I spent a long time saying, “I’m going to focus on the research. I’m going to get these big results. I’m going to become a famous scientist, a famous mathematician.” And I woke up years later and realized, what’s the point? I could spend my whole life doing research, but what am I really doing if I don’t have a life outside of that? I’d say that’s perhaps my biggest failure.

The second thing is, I think I consider taking a job at Purdue University in West Lafayette, Ind., a failure. I knew within my first year that it wasn’t going to work.

I grew up in southern California, a large, sprawling metroplex. There’s lots to do, lots to see — beaches, mountains, the movie culture, the car culture, all of this. Indiana has none of that. There are no large cities, no mountains. And for most people — you go to work, go home at 5 p.m., spend time with your family, that’s it. People don’t go out. And if you’re someone like me who didn’t have a family, you can find that a very difficult place to live.

Also, I hate to say it this way, but Indiana is a racist state. I’m not saying California is not, but you can’t be Black in this country and not know that the resurgence of the Ku Klux Klan was in Indiana back in the 1920s. And you see that everywhere. There are Confederate flags. There are these so-called “sundown cities” where, even to this day, if you’re Black, it’s dangerous to be in that town after sundown.

Also, in my department there wasn’t a lot of collegiality. People were there to work. And when they were done, they went home. There really wasn’t a sense of, maybe we can work together, maybe we can make this a more interesting department.

Science is not something you do in a bubble. You don’t just come up with a great result, publish a paper and become famous. I had a hard time finding people to collaborate with. Even in areas where I was considered the expert outside of Purdue, people there weren’t willing to listen to me.

Yet I kept telling myself, I can find a way to make this work. I am a problem solver. I eventually did make full professor. But of the two to three thousand faculty at Purdue, only 20 to 30 were Black. And only about 10 of us were full professors. That’s less than 1 percent. When I realized I was in such a small minority, that’s when I really did respect that it was very difficult to make it to that high of a rank. Ultimately, I realized that I had no reason to do this anymore. I had nothing more to prove. 

What’s one of your biggest successes?

A big success for me today is being able to be back here in Los Angeles to help take care of my parents. That may sound a bit silly, but often we’re in a culture where people think a scientist or mathematician has to be the crazy person locked up in a room working by ourselves. I bought into that for a long time, thinking it doesn’t matter where you live or what kind of life you have — that all that’s important is doing the math. 

But as I watched my parents get older, I realized it would be nice if I could be around to help them. Little things like taking them out to the movies, taking them to restaurants and amusement parks and other places. It’s comforting to know that, yes, I’m here at work. Yes, I’m teaching classes. Yes, I’m mentoring students. But when everything’s done, I can go home and spend time on weekends knowing I’m there to help my parents also have a good life.

How do you get your best ideas?

I think I get them by being an information junkie. I love to watch documentaries. I will turn on PBS. I will turn on the History Channel. I love science and discovery. Watching documentaries gives me ideas of how things work. 

I also like attending conferences where I watch other mathematicians give presentations on their research. I don’t always understand what people are saying, but there’s always one equation they’ll show that gets me thinking, “Where did I see that before?” Then I start making connections and trying to figure out why they would use this equation here whereas others use it in a completely different context. What’s the relationship? 

I try to get information anywhere and everywhere. And eventually I start seeing how these things are all related.

What do you do in your spare time?

I’m big into watching movies. Any kind of movie — small independent films, large blockbuster films. I get into conversations with my students about movies all the time. I think 1917 was one of the best movies in recent memory. I’m a big fan of the Avengers — the whole Marvel cinematic universe and the 20-some-odd movies that have come out over the last 10 years.

Also, there are things I did quite a bit when I was younger but haven’t really done the last 10 years. I’ve now gotten back into playing classical piano.

What piece of advice do you wish you had been given when you were younger?

Try to determine what your passion is — not necessarily something you’re good at, but something you really like.

This Q&A is part of a series exploring the many paths to a career in science, technology, engineering and mathematics (STEM). It has been made possible with generous support from Arconic Foundation.

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Organic Chemical make up Basic Rules and methods Biochemistry Part 12

Saxon Numbers Explained

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For being effectively prepared for his or her university entrance exam (elizabeth.h., Lay or perhaps ACT) scholars have to full Innovative Arithmetic for their younger 12 months. Saxon publications are generally skill-level books, definitely not grade-level guides. Whatever the case, they are the not one but two solutions I might offer somebody that ended up being requesting if they could miss a level. I check and also class their newspaper. Learners who finish Advanced Mathematics may have obtained the equivalent of two semesters involving geometry, a single semester with trigonometry, and something session of sophisticated geometry.

2 scholar workbooks plus One fact minute card collection. Consumable, non-reproducible workbooks. Class creating types may also be integrated, in addition to common examination styles.

Math 87 includes a wide variety connected with themes which might be necessary for the mathematical requirements of numerous expresses. Substantial pre-algebra content is included, and scholars whom comprehensive the writing efficiently (80% and up exam scores) will likely be able to carry Algebra 1 for their next math concepts course.

Algebra 1/2 is targeted on producing expertise of which prepare yourself individuals to get geometry. The pre-algebra content articles are additional comprehensive versus the pre-algebra information involving Math Eighty seven; even so, the particular scope is less wide.

Math 87 insures a diverse assortment associated with issues which have been needed by the exact expectations for many claims. Sizeable pre-algebra content is involved, and also college students who finish the text effectively (80% and up exam scores) will likely be prepared to acquire Algebra 1 as his or her future math study course.

2 student workbooks and One reality cards fixed. Palatable, non-reproducible workbooks. College class saving forms will also be bundled, as well as verbal assessment sorts.

2 undergraduate workbooks as well as Just one fact cards arranged. Safe to eat, non-reproducible workbooks. College class producing varieties also are provided, coupled with dental review styles.

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*** These kinds of students might find the information presented inside Advanced Mathematics tricky. Most of us moved to your third courses, but it surely was repeating together with apparently unlimited websites connected with troubles, certainly one of this daughters could lose hope at the prospective client of having to perform math everyday. Merely couldn’t need a whole lot repetition with it. Some with the worksheets viewable are generally College student edition saxon arithmetic, Saxon arithmetic Seventy six, Regular lesson plans intended for, Saxon, Saxon arithmetic study course 1 document, Saxon algebra i actually 1 / 3 version, Specifications success, Position test out regarding. Possibly at the end of the season, we nonetheless received most of your worksheet web sites remaining. This “Lesson Preparation” box at the outset of every entry makes it simplallows you setting all the things inside the night before which means that your consultations operate correctly. They may be truly recouping degrees inside Algebra One and a couple in comparison with would inside Saxon 8/7.

Teachers Acitivities

The child is finishing up Algebra 2, well, i would not have personal experience recent that. Instructing math concepts through the a number of hands-on manipulatives, the offer is designed for pupils who’ve your kinesthetic mastering style. Stressing research along with interpersonal reports contacts, Numbers 3 or more utilizes models as well as video game titles that will help your own students comprehend and exercise fresh concepts. With your course game titles lets quicker pupils who aren’t thriving with Advanced Mathematics during the 10th level to test all over again and still acquire credit history. That would be deemed a typical skill level, bearing in mind the program higher than is ideal for pupils who do very well together with numbers.

Homeschool Specialists’ Spotlights

Saxon Math Tutorials A person, 3, and 3 add as well as propagate standard items, giving pupils time for you to study and exercise skills all year long, grasp content material, and grow higher-order contemplating. Pre-Calculus I includes the first 70-90 instruction in Advanced Numbers. Pre-Calculus A pair of comprises the remaining instructions. My own boy is finishing up Algebra Only two, i really do not have personal experience previous that will. Your entry to this page appeared to be hindered by Wordfence, a burglar service provider, which shields web pages through vicious activity. As long as they continue to do not have an accurate solution each to the Mp3, go through the dilemma as well as Dvd educator talks about how to work the problem. * Advised system headings. We love to the pliability of Sonlight and in what way the book selections is usually loved by the extensive age group.

I considerably treasured the particular scripted instructor’s guide. My partner is sweet in math and may assistance him having complicated troubles. Plus, you’ll not locate websites involving apparently with their almost endless assessment on the very same notion. If they were built with a great deal of punition, next I might acquire often be their project for the entire day, virtually no new tutorial, as well as I’d personally add to that some of the worksheet websites.

Saxon Numbers Explained

As long as they experienced a lots of improvements, then I would obtain that always be their particular job throughout the day, no completely new lesson, in addition to I would add to that a couple of the worksheet webpages. We like precisely how Sonlight helps you to raise Good Fee youngsters. Success! This is a summary of how you would completed it. I’m going to conduct a different up-date in a couple decades! Worksheet can wide open in the brand-new windows. UPDATE 3: (June 2014) My own earliest baby is merely establishing his senior citizen https://collegehelp.club/pay-for-college-papers/ year. I had been thinking about conducting a submit about definitely the home-school curriculum, however, when a person talked about some queries this morning regarding Saxon Numbers I actually knew it will be an excellent subject matter to write down concerning.

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Steam Autumn Sale Kicks Off, Joined By Initially Yearly Steam Awards

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